Too bad that the basics of category theory aren't taught in school. But then again, the educational system doesn't care much about the philosophy of mathematics or the foundations of mathematics. — ssu
I agree that calculus can work quite well with the concepts of unboundedness and potential infinity, but 'actual' infinities are implicitly assumed throughout the standard treatment. — keystone
As I have said before, I have written many papers and notes without ever becoming transfinite. — jgill
Have you written calculus papers/notes that are not (implicitly or explicitly) built upon infinite sets like R? — keystone
But that program (even in an infinite world*) cannot actually output a set with a cardinality of ℵ0. Potential is important and I feel like it's been forgotten in our Platonist world. — keystone
I think the whole idea grossly overestimates people's interest in having an opinion on every political subject all the time — Benkei
By moving the focus from the destination to the journey the need for actual infinity vanishes. — keystone
In my recent posts, I have been establishing that real numbers instead describe potential k-curves, which can be thought of as yet to be constructed k-curves which when constructed have the potential to be arbitrarily small (but always retain a non-zero length). — keystone
Of course it is true you're not obliged to find that interesting. — Wayfarer
The challenge for scientific realism is the concept of superposition — Wayfarer
Quantum superposition is a fundamental principle of quantum mechanics that states that linear combinations of solutions to the Schrödinger equation are also solutions of the Schrödinger equation. This follows from the fact that the Schrödinger equation is a linear differential equation in time and position. More precisely, the state of a system is given by a linear combination of all the eigenfunctions of the Schrödinger equation governing that system.
He ends up advocating (maybe just "showing the benefits of" is a better term) of an approach grounded in category theory. — Count Timothy von Icarus
Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of the wave function, the quantum-mechanical characterization of an isolated physical system.
Question from the stands: are individual numbers considered objects? — Wayfarer
What would be the mathematical object behind/described by the "well ordering theorem" — ssu
I think the one issue in mathematics is that defining a "mathematical object" can be difficult if there are equivalencies, multiple ways of representation of the "object". There's a whole field of mathematics just looking at these similarities, category theory. — ssu
What's wrong with a democratic nation deciding how much immigration it wants to let in? — Philosophim
What can the head of a mathematics department say when accused that there are too few if any women or minorities represented in the staff? Stop hiring your male buddies and follow the implemented DEI rules! — ssu
I would like to go back to the actual topic of this thread. — ssu
Is the "parole" plan in 3. above a reasonable policy? I think not. — jgill
Can I ask why you think this and what you think should be done differently? — Samlw
The only objects in these graphs that can be 'cut' are the edges — keystone
I find myself defending a hill that I'm definitely not willing to die on. If it made a difference to anyone, I'd gladly deny, renounce, disavow, and forswear my earlier claim that "Math is what mathematicians do." It was a throwaway line, a triviality, a piece of fluff — fishfry
Yes I know these people. How bad has it gotten when Scientific American, of all outlets, publishes Modern Mathematics Confronts Its White, Patriarchal Past. — fishfry
..the first step is to accept that k-curves are indivisible. k-vertices in these graphs cannot be partitioned — keystone
A good idea often begins with some handwaving as it's being formed, but through refinement and rigorous thought, it can mature into a precise and well-supported explanation. — keystone
You seem not to understand how the mathematical method of handwaving works — TonesInDeepFreeze
BaDbE can be unified into BaC because DbE can be treated as a whole that captures all the structure of C. In other words — keystone
I have two continua described by Graph 1 and Graph 2, respectively. — keystone
But you seem to be using visualization software in your images. They didn't have that stuff when I was in school — fishfry
Oh. Interesting — fishfry
If this is true, then we can assume that there is quantum entanglement between the brains of related individuals in nature — Linkey
However, my primary focus is on the objects themselves, such as the Cartesian coordinate system. I believe this system needs a parts-from-whole, continuum-based reinterpretation, as the current understanding relies heavily on the notion of actual infinity. — keystone